2017/10/23 by Fusheng Deng, Deng, Fusheng, John Erik Fornæss +1
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1710.08046
openalex publication_date 2017/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct examples of flat fiber bundles over the Hopf surface such that the total spaces have no pseudoconvex neighborhood basis, admit a complete Kähler metric, or are hyperconvex but have no nonconstant holomorphic functions. For any compact Riemannian surface of positive genus, we construct a flat \mathbb P1 bundle over it and a Stein domain with real analytic bundary in it whose closure does not have pseudoconvex neighborhood basis. For a compact complex manifold with positive first Betti number, we construct a flat disc bundle over it such that the total space is hyperconvex but admits no nonconstant holomorphic functions.